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On Grassmann $4$-designs
Abstract
We prove that there is a unique tight $4$-design in the real Grassmannian G2,4, up to the action of O(4). Using symmetric association schemes, we also construct an N-point $4$-design in G2,4 for every even integer N≥10. For symmetric association schemes of order less than $21$, we classify the pairs of rank-three primitive idempotents defining injective maps into G2,4; their images are Grassmannian $4$-designs precisely for four schemes of order $16$.
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BibTeX
@misc{baladram2026grassmann,
title = {{On Grassmann $4$-designs}},
author = {Mohammad Samy Baladram and Ryutaro Misawa and Akihiro Munemasa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08047},
eprint = {2611.08047},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08047},
}
RIS
TY - UNPB
TI - On Grassmann $4$-designs
AU - Mohammad Samy Baladram
AU - Ryutaro Misawa
AU - Akihiro Munemasa
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08047
UR - https://arxiv.org/abs/2611.08047
AB - We prove that there is a unique tight $4$-design in the real Grassmannian G_2,4, up to the action of O(4). Using symmetric association schemes, we also construct an N-point $4$-design in G_2,4 for every even integer N≥10. For symmetric association schemes of order less than $21$, we classify the pairs of rank-three primitive idempotents defining injective maps into G_2,4; their images are Grassmannian $4$-designs precisely for four schemes of order $16$.
ER -